Hi,
I have a red sea 625 L display, and when I set it up I didn't run my skimmer for a while as I didn't want to bottom out my nutrients. I got an o2 test kit and tested my disolved oxygen which showed it was roughly 5 ppm, which I wanted to increase. I got a fairly big airstone and air pump and set it up in my sump, before the bubble trap for my return pump, I had no issues with increased microbubles like some people say you will have. I ran this air stone all the time and tested o2 regurlarly and noticed no difference in mesured level. I then ended up turning my skimmer on and tested o2 again with it running and it put my o2 levels up to 6/7 ppm. I thought that it was a good idea the airstone but in practice it didn't really do anything based on my testing. I think that because my take is a 625L system, the airstone was just too small to have a noticable effect. When comparing the amount of bubbles from the skimmer to the airstone I had there was a lot more from the skimmer. Also when my o2 was 5ppm, there was no signs of low oxygen in fish, like rapid breathing or swimming at top of tank, so it seems that running without skimmer still has enough oxygen for fish.
Only thing that may alter my results is that my tank was not done cycling, meaning that bacteria was rapidly colonising and I would imagine using up a lot more oxygen to break down elevated levels of ammonia and nitrite during cycle, so possibly my o2 levels could have dropped lower but because I had the airstone they stayed stable at aroun 5ppm instead. Just a thought